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what is the identity element in multiplication?

An automobile dealership uses CODE = 1 for new automobiles, CODE = 2 for used automobiles, and CODE = 3 for separate accessories. A salesman’s commissions are as follows: on new automobile, 3% of the selling price but a maximum of $300; on used automobile, 5% of the selling price but with a minimum of $75; on accessories, 6% of selling price.

1. Draw a flowchart that inputs CODE and PRICE and outputs COMMISSION.

2. Write a pseudocode programme that inputs CODE and PRICE and outputs COMMISSION.

1. Draw a flowchart that inputs CODE and PRICE and outputs COMMISSION.

2. Write a pseudocode programme that inputs CODE and PRICE and outputs COMMISSION.

sum <-- 2 * n + 404

for (int i==1; i < n + 1; i++ ) do

sum <-- sum + i + MyA[i] + 404

for (int j = 0; j <= i; j++) do

sum <-- sum * MyA[j] + i + 404 * n

end-for (j)

for (int k = 0; k <= n; k++) do

sum <-- sum * k + MyA[k]

end-for (k)

sum <-- sum + 303

end-for(i)

sum <-- sum + 303 * n

Find an explicit expression for T(n), the count function for the number of times that your operation is executed (is a function of n). It likely starts with one more summations, and ends with a polynomial in n in standardized form (i.e. simplest terms). Show work.

for (int i==1; i < n + 1; i++ ) do

sum <-- sum + i + MyA[i] + 404

for (int j = 0; j <= i; j++) do

sum <-- sum * MyA[j] + i + 404 * n

end-for (j)

for (int k = 0; k <= n; k++) do

sum <-- sum * k + MyA[k]

end-for (k)

sum <-- sum + 303

end-for(i)

sum <-- sum + 303 * n

Find an explicit expression for T(n), the count function for the number of times that your operation is executed (is a function of n). It likely starts with one more summations, and ends with a polynomial in n in standardized form (i.e. simplest terms). Show work.

Determine the spacing h in a table of equally spaced values for the function f(x)= (2+x)^4 , 1≤x≤2 so that the quadratic interpolation in this table satisfies | error|≤ 10^-6

determine a unique polynomial f(x) of degree<=3 such that

f(x_0)=1, f'(x_0)=2, f(x_1)=2, f'(x_1)=3 where x_1 - x_0 = h

f(x_0)=1, f'(x_0)=2, f(x_1)=2, f'(x_1)=3 where x_1 - x_0 = h

Using Xo = 0 find an approximation to one of the zeros of x^3 − 4x +1 = 0 by using Birge Vieta Method. Perform two iterations

Are the following TRUE or FALSE. explain

n2 = O(n2)

n3 = O(n2)

n log n = O(n2)

n2 = O(n log2 n)

n2 = O(n2)

n3 = O(n2)

n log n = O(n2)

n2 = O(n log2 n)

Consider the graph G0 with 3 components which are triangles. G0 has 9 vertices labeled A to I and 9 edges (A, B), (B, C) … as shown below.

If each vertex of G0 is assigned a red or a green color, then we say that an edge is colored if its ends have different colors.

Ajai and Rekha color the vertices of G0 in the following manner. Ajai proposes a color (red or green) and Rekha chooses the vertex to apply this color. After 9 turns, all the vertices of G0 are colored and the number of colored edges is counted.

Suppose Ajai would like to maximize the number of colored edges while Rekha would like to minimize the number of colored edges. Assuming optimal play from both players, how many edges will be colored? Explain your reasoning.

If each vertex of G0 is assigned a red or a green color, then we say that an edge is colored if its ends have different colors.

Ajai and Rekha color the vertices of G0 in the following manner. Ajai proposes a color (red or green) and Rekha chooses the vertex to apply this color. After 9 turns, all the vertices of G0 are colored and the number of colored edges is counted.

Suppose Ajai would like to maximize the number of colored edges while Rekha would like to minimize the number of colored edges. Assuming optimal play from both players, how many edges will be colored? Explain your reasoning.

Give the most compact theta notation for the number of times the statement

x = x + 1 is executed in the following pseudo-code:

for i = 1 to i = 3n − 1{

for j = 1 to j = n{

x = x + 1

}

}

x = x + 1 is executed in the following pseudo-code:

for i = 1 to i = 3n − 1{

for j = 1 to j = n{

x = x + 1

}

}

Let f(n) and g(n) be functions with domain {1, 2, 3, . . .}. Prove the following:

If f(n) = Ω(g(n)), then g(n) = O(f(n)).

If f(n) = Ω(g(n)), then g(n) = O(f(n)).